Problem 179 - Prealgebra

Question

In the following exercises, subtract and then check by adding. $$ 2,150-964 $$

Step-by-Step Solution

Answer

2,150 - 964 = 1,186. Verification: 1,186 + 964 = 2,150.

Step 1: Set Up the Problem

Write the numbers in a column format aligning them by place value, with 2,150 on top and 964 beneath it.

Step 2: Subtract the Units Place

Subtract the digits in the units place: 0 - 4. Since 0 is less than 4, borrow 1 from the next place value. This makes 10 - 4 = 6.

Step 3: Subtract the Tens Place

Subtract the tens place: 4 (after borrowing) - 6 = 8. Since 4 is less than 6, borrow 1 from the hundreds place. This makes 14 - 6 = 8.

Step 4: Subtract the Hundreds Place

Subtract the hundreds place: 0 (after borrowing) - 9. Since 0 is less than 9, borrow 1 from the thousands place. This makes 10 - 9 = 1.

Step 5: Subtract the Thousands Place

Subtract the thousands place: 1 (after borrowing) - 0 because we borrowed from the thousands place. Thus, we get 1.

Step 6: Write Down the Result

Combine the results from each place value to get the final subtraction result: 2,150 - 964 = 1,186.

Step 7: Verify by Addition

To check the subtraction, add the result (1,186) to 964. If the sum is equal to 2,150, the subtraction is correct: 1,186 + 964 = 2,150.

Key Concepts

arithmetic operations

In mathematics, arithmetic operations are the foundation for many other concepts. When we talk about subtraction with borrowing, understanding arithmetic operations is crucial. Subtraction is taking one number away from another. Borrowing occurs when a number is too small to subtract from. For example: if we have 0 - 4, we can't subtract it directly because 0 is less than 4. This is why we borrow from the next higher place value to make the subtraction possible. Let's break it down: * We begin by aligning the numbers by their place values. * We start subtracting from the rightmost place. * Whenever the top number is smaller, borrowing happens from its left neighbor. This ensures that subtraction is performed correctly. Remember to always check your work by adding the result back to the number you subtracted from.

place value alignment

Place value alignment is key when handling subtraction with borrowing. Ensure each digit sits directly above or below its counterpart: units under units, tens under tens, and so on.

• Start writing the larger number (2,150) on top and the smaller number (964) beneath it.
• Align each digit according to its place value: thousands, hundreds, tens, and units.

This alignment method guarantees that each digit operates within its correct place value during subtraction, essential for accurate calculations. Misalignment can lead to incorrect subtraction, especially when borrowing. Example: For 2,150 – 964, write:
2150
0964

verification by addition

Verification by addition is a simple yet powerful method to ensure your subtraction result is correct. Once you have obtained the subtraction result, you can verify it by adding this result to the subtracted number. For instance:

• We got 2,150 - 964 = 1,186 after performing subtraction.
• Now add 1,186 + 964. If your addition result is the same as the original number, your subtraction is correct.

Example:
1186
+ 964
= 2150 This process helps ensure that no mistakes were made in the steps taken during subtraction and provides peace of mind that calculations are accurate. It is a helpful habit when dealing with more complex arithmetic problems.